The nouns corollary and correlation are often confused, yet their meanings are different and their origins separate.
Corollary
Corollary has roots in the Latin corollarium, meaning money paid for a garland, or gratuity. In modern English, a corollary is an obvious deduction, a natural consequence, or a proposition that follows with little or no proof from one already proven. For example, these writers use the word well:
Unmentioned in the debate over threatened school budget cuts and an income tax proposed to avert them is the potential corollary of swollen class sizes and shrunken staff numbers … [The Register-Guard]
He argues that the right of biological parents to keep and raise the child they produce is a corollary of a more general right, which is, to be allowed to finish what one has begun. [Metapsychology]
A corollary to Huckabee’s unwillingness or inability to put together a serious organization is his unwillingness or inability to put the pieces in place to raise the tens of millions he would need to compete seriously. [Washington Post]
In each of these cases, the corollary is an obvious result of something else.
Correlation
Correlation means literally to relate together. A correlation is a causal, complementary, parallel, or reciprocal relationship between two comparable entities. Correlation usually takes the preposition between; corollary should never use between.
These writers use correlation well:
Despite traditional negative correlation, gold and USD has been moving in tandem since the outbreak of the anti-government unrest in Egypt. [International Business Times]
Never mind that there’s no correlation between state fiscal health and whether public employees can unionize. [Harvard Crimson]
